At the risk of repeating earlier posters, don't get either in my opinion. Neither are particularly powerful, and depending on the revision of the MP, it may even be less powerful in some ways than your Air. Certainly, if you're going for graphics, I'm not sure any G5 dedicated card is substantially more powerful than even the HD4000 (if at all... it might be worse).
If you don't mind me asking, what is your budget? If I were you, I'd wait until the next gen Haswell Mini and just get that. Its CPU should be on par with the current generation Mac Pro (as the current Mac Pros are really two generations old) and HD5000 supposedly will double 4000 performance and be comparable to low/mid-end discreets (key word being supposedly).
This kinda thing is not really what i believe in. I love desktop computing with a full tower workstation. You have a mac pro, you can upgrade the Xeons, you have two of them, and you have about a billion open spaces for dimms, well only 8 but whatever :3
Also, you can put monster graphics cards in there too. Not only can you do this, but you can put multiple. And if you use eyefinity cards, you can run 12 displays. Mac mini, 2 displays.
So lets sum this up:
Mac mini:
Max ram: 16GB
Max GPU: intergrated <-- lol
Max CPU: best i7 mobile quad core
Max Displays: 2, (unless thunderbolt but w.e.)
Max HDD: Various fusion drive options
Expansion slots: Nope ^.^
Little blower cooling, keeping your whole machine nice and warm.
Mac Pro:
to start off, 980w psu.
Max ram: 64GB, processor config dependant
Max CPU: im not so good with xeons. but, 12 Cores of Xeon. 2x 6 core CPUs.
Max GPU: Any GPU really, but supports GTX 680, HD7970 GHz edition, among others. No dual GPU Card support, as crossfire and SLi are not supported under OSX.
Max Displays: again depends on GPUs, but use two eyefinity cards, and you got 12 displays.
Max HDD: 4x 3.5/2.5" solutions of your choosing. Use 4 x 4TB drives and you got 16TB right there.
Cooling, several cooling zones, designed to be dead silent, and it works, whole machine is whisper quiet, keeping everything chilled.
Expansion: ahh, love this one. PCI Express lanes, you can put raid cards, and connect to an external raid solution, USB cards, esata, you name it.
Also, not to mention the extra outputs on a Pro, such as Optical audio in and out, Several firewire ports, many USB ports, and dual gigabit ethernet, the last one there being one of my favourites, having so many dang networks around my house ^.^
So, who wins?
Take a 2006/7 Mini, it will be slow and sluggish for the most part, using a core solo or core duo.
Take a Mac Pro 2006/7 and slap a $70 GPU in that guy, and you've got a screamer right there.
Buy a mini today, it'll last a few years.
Buy a pro today, and as we've seen the 2006 models so, it'll last 7 years. However even longer than that with upgrades but no new OS.
Heck, I'm still using snow leopard and loving it, why is everyone so stressed about OS upgrades? Chill people.